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Bunuel
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Bunuel

Tough and Tricky questions: Overlapping Sets.



At a certain company, some of the employees have advanced degrees, some have one year or more of work experience, and some have both. If 20 percent of all employees have one year or more of experience and no advanced degree, what percentage of employees have advanced degrees and less than one year of experience?

(1) 35 percent of the employees do not have advanced degrees and 55 percent have less than one year of work experience.

(2) 15 percent of the employees do not have advanced degrees and one year or more of work experience, but 45 percent have one year or more of experience.

Kudos for a correct solution.

Sorry I didnot get option for creating table...

| Degree | No Deg | Total
-----------------------------------------------------------
EX >=1 | 20t/100 |
-----------------------------------------------------------
EX<1 X | |
-----------------------------------------------------------
Total | | T
------------------------------------------------------------

We need to find X*100/T --> where T is total number of employees

(1) 35 percent of the employees do not have advanced degrees and 55 percent have less than one year of work experience.

| Degree | No Deg | Total
-----------------------------------------------------------
EX >=1 25T/100 | 20t/100 | 45T/100
-----------------------------------------------------------
EX<1 X | | 55T/100
-----------------------------------------------------------
Total 65T/100 | 35T/100 | T
------------------------------------------------------------

So, X=65T-25T/100 = 40/100T Ans : 40% ---> Suff

(2) 15 percent of the employees do not have advanced degrees and one year or more of work experience, but 45 percent have one year or more of experience.


| Degree | No Deg | Total
-----------------------------------------------------------
EX >=1 | 20t/100 | 45T/100
-----------------------------------------------------------
EX<1 X | 15T/100 | X+15T/100
-----------------------------------------------------------
Total | | T
------------------------------------------------------------

T= X+15T/100+45T/100 = X+60T/100 =T
Again we get X=40% --> Suff

IMO -- D

Please correct me if I am wrong
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Lets degree= D
No degree= ND
1 or more year workex =MW
1 or less year workes = LW
Total = T

Forming a table :


From statement 1

D ND T

MW

LW 35 20 55

T 35 100

Answer is 35% . SUFFICIENT.

From statement 2



D ND T

MW 15 45

LW 35 20 55

T 35 100

Answer is 35%.

Both statement can solve this riddle.


Answer is D
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I draw double matrix to solve this one

Advanced Degree/No adv Degree Total
less 1 year X 15% 55%
more than 1 year 20% 45%
Total 35% 100%

We know that 20% have more than 1 year experience and No adv Degree.
1. We know that 35% do not have adv Degree and 55% have less that 1 year work experience. Hence we can find that 15% have less that 1 year and no adv Degree and thus we can find how many have Advanced Degree and less than 1 year. Sufficient
2.Since we know that 45% have more than 1 year experience we can conclude that 55% have less than 1 year. And we know that 15% Do not have Adv degree and more than 1 year (i.e do not have both). We can find x. Sufficient
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(2) 15 percent of the employees do not have advanced degrees and one year or more of work experience, but 45 percent have one year or more of experience.

For statement 2, if you say 15% DO NOT have advanced degree or work ex, it doesn't mean they have neither. It means they do not have both, which is the intersecting part. They can have either have advanced degree or work ex or none.

Statement like "15% employees neither had advanced degree nor one year or more of work experience" would have been better
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for statement 2, why are we not conidering the case where there is some % of people who only have advanced degree?
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for statement 2, why are we not conidering the case where there is some % of people who only have advanced degree?

For employees with an advanced degree, there are only two possibilities: they have less than 1 year of experience or they have 1 or more years of experience. There’s no other category. Here’s what we know when considering Statement 2.



Hope it helps.
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